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College Algebra 7th Edition Robert F Blitzer - Solutions
Factor the expression completely. axbxay + by
Clear fractions and solve. Check your answers. + X 1 x-1 x
Clear fractions and solve. Check your answers. 1 x + 3 2 - 2 x - 3 1 x-3
Clear fractions and solve. Check your answers. 4 x-5 1 x+5 1
Factor the expression completely. 18x² + 12x + 2
Clear fractions and solve. Check your answers. 1 2 x-4 1 x + 4
Factor the expression completely. -3x² + 30x75
Clear fractions and solve. Check your answers. 2a 1 1 26 1
Factor the expression completely. -4x³ + 24x² - 36x
Factor the expression completely. 27x³-8
Factor the expression completely. -x²8x
Clear fractions and solve. Check your answers. 1 2 1 I 1 2y² 1 3+²
Factor the expression completely. 27x³ + 8
Factor the expression completely. x² + 3x³ + x + 3
Factor the expression completely. x42x³x + 2 - -
Factor the expression completely. x² + 3x³ + x + 3
In Exercises 61–68, use the graphs of {an} and {bn} to find each indicated sum. The Graph of {a} an -1 1. 23 st 50 ITT 20 3 4 5 HA n The Graph of {b} b₁ 4 1 1 -2 ….….……….…….….…….……………… +5 2 3 4 5 n
You are offered a job that pays $30,000 for the first year with an annual increase of 5% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.05 times what it was in the previous year. What can you expect to earn in your sixth year on the job?
In Exercises 68–69, write the first three terms in each binomial expansion, expressing the result in simplified form.(x2 + 3)8
A company offers a starting yearly salary of $33,000 with raises of $2500 per year. Find the total salary over a ten-year period.
A ball is thrown vertically upward from the top of a 96-foottall building with an initial velocity of 80 feet per second. The height of the ball above ground, s(t), in feet, after t seconds is modeled by the position functiona. After how many seconds will the ball strike the ground?b. When does the
In Exercises 37–44, find the sum of each infinite geometric series. 1 1 1 2 + 1 4 1 8 +
In Exercises 29–42, find each indicated sum. 5 (i + 2)! i! i=1
Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥ m. Use this extended principle of mathematical induction to prove that each
In Exercises 37–44, find the sum of each infinite geometric series. 3 −1+ 1 1 3 9
Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135, . . . .
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability thatyou are dealt a 2 or a 3.
In Exercises 39–48, find the term indicated in each expansion.(x - 1)9; fifth term
The bar graph shows online ad spending worldwide, in billions of dollars, from 2010 through 2015. Develop a linear function that models the data. Then use the function to make a projection about what might occur after 2015. Online Ad Spending (billions of
Use the formula for nPr to solve Exercises 41–48.A corporation has ten members on its board of directors. In how many different ways can it elect a president, vice president, secretary, and treasurer?
In Exercises 37–44, find the sum of each infinite geometric series. 00 Σ 8(-0.3) -1 i=1
Find the sum of the first 80 positive even integers.
In Exercises 43–44, find S1 through S5 and then use the pattern to make a conjecture about Sn. Prove the conjectured formula for Sn by mathematical induction. 1 + 4 12 24 Sn: + 1 2n(n + 1) =
The current, I, in amperes, flowing in an electrical circuit varies inversely as the resistance, R, in ohms, in the circuit. When the resistance of an electric percolator is 22 ohms, it draws 5 amperes of current. How much current is needed when the resistance is 10 ohms?
In Exercises 43–45, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum. 6 i=1 5¹
Find the sum of the first 7 terms of the geometric sequence: 8, 4, 2, 1, . . . .
Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥ m. Use this extended principle of mathematical induction to prove that each
In Exercises 37–44, find the sum of each infinite geometric series. 00 Σ 12(-0.7) -1 i=1
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability thatyou are dealt a red 7 or a black 8.
In Exercises 39–48, find the term indicated in each expansion.(x - 1)10; fifth term
In Exercises 43–45, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum. 7 Σ 3(-2) i=1
In Exercises 43–44, find S1 through S5 and then use the pattern to make a conjecture about Sn. Prove the conjectured formula for Sn by mathematical induction. 1 Sa: (1-2)(1-3)(¹-) (1 - ² + ₁) = ? n+1) 4
Use the formula for nPr to solve Exercises 41–48.For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?
Find the sum of the even integers between 21 and 45.
In Exercises 39–48, find the term indicated in each expansion. (x - 1); fourth term
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation12 + 22 + 32 +....+ 152
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 17 i=1 (5i + 3)
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.5 5 5 + 10 100 + 5 1000 + 5 10,000 +
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability thatyou are dealt a 7 or a red card.
In Exercises 39–48, find the term indicated in each expansion.(x2 + y3)8; sixth term
In Exercises 39–48, find the term indicated in each expansion.(x3 + y2)8; sixth term
In Exercises 45–46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again.Find the probability that the pointer will stop onan odd number or a number less than 6. 7 8 5 1 4 2 3
Use the formula for nPr to solve Exercises 41–48.Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 20 movies during the year, in how many ways can the three best be chosen and ranked?
Find the sum of the odd integers between 30 and 54.
In Exercises 43–45, use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum. 114 -1
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation14 + 24 + 34 +......+ 124
In Exercises 45–46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again.Find the probability that the pointer will stop onan odd number or a number greater than 3.
In Exercises 39–48, find the term indicated in each expansion. (x + 1); fourth term 2
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 20 Σ (6 – 4) W i=1
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability thatyou are dealt a 5 or a black card.
In Exercises 46–49, find the sum of each infinite geometric series. 9 +3+1+ 3 +
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. O.1 = 1 + 10 1 + 100 1 1 1000 10,000 ` + +
Use the formula for nPr to solve Exercises 41–48.In a race in which six automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation2 + 22 + 23 +........+ 211
Determine whether the values in each table belong to an exponential function, a logarithmic function, a linear function, or a quadratic function. ล. X 0 1 2 3 4 ล y 7 4 1 -2 -5 b. X 0 1 2 3 4 0 ล y 1 4 16 64 256
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 30 Σ (-3i + 5) i=1
Show that B is the multiplicative inverse of A, where 3 A = ²₁₂2] and B = [-² 1 -1 2 -3 2
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.47 = 47 + 100 47 10,000 + 47 1,000,000 +
Fermat’s most notorious theorem, described in the section opener on page 782, baffled the greatest minds for more than three centuries. In 1994, after ten years of work, Princeton University’s Andrew Wiles proved Fermat’s Last Theorem. People magazine put him on its list of “the 25 most
In Exercises 46–49, find the sum of each infinite geometric series. 2-1 + 1 −2 1 4
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation5 + 52 + 53 +......+ 512
In Exercises 39–48, find the term indicated in each expansion.(x2 + y)22; the term containing y14
Use this information to solve Exercises 47–48. The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person isA
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 40 M ∑(-2i + 6) i=1
In Exercises 46–49, find the sum of each infinite geometric series. -6 + 4 8 16 + 3 9 00 | دا
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.83 83 + 100 83 10,000 83 1,000,000
Use the formula for nPr to solve Exercises 41–48.Nine bands have volunteered to perform at a benefit concert, but there is only enough time for five of the bands to play. How many lineups are possible?
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation1 + 2 + 3 +....+ 30
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.257
In Exercises 39–48, find the term indicated in each expansion.(x + 2y)10; the term containing y6
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 100 Σ i=1 4i
Use this information to solve Exercises 47–48. The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person isA
In Exercises 46–49, find the sum of each infinite geometric series. 00 Σ 5(0.8) i=1
Use the formula for nPr to solve Exercises 41–48.How many arrangements can be made using four of the letters of the word COMBINE if no letter is to be used more than once?
Graph the hyperbola whose equation is 25x2 - 16y2 - 100x - 96y - 444 = 0. Where are the foci located? What are the equations of the asymptotes?
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation 1 2 + 2/3 + 3 4 + + 14 14 + 1
Exercises 49–51 will help you prepare for the material covered in the next section. Each exercise involves observing a pattern in the expanded form of the binomial expression (a + b)n.Describe the pattern for the exponents on a. (a + b)¹ = a + b (a + b)² = a² + 2ab + b² (a + b)³ = a³ +
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation1 + 2 + 3 +....+ 40
In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form.(x3 + x-2)4
In Exercises 45–50, express each repeating decimal as a fraction in lowest terms. 0.529
For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 50 ∑(-4i) i=1
In Exercises 49–52, a single die is rolled twice. Find the probability of rollinga 2 the first time and a 3 the second time.
In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form. x-³) 3
Use the formula for nCr to solve Exercises 49–56.An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?
Use the graphs of the arithmetic sequences {an} and {bn} to solve Exercises 51–58.Find a14 + b12. bn "D 100 PA LOO CN 00 C n n 910 G menja ह्म प्रै HH
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation 1 2 + 3 4 + 3 + .+ 16 16 + 2
Exercises 49–51 will help you prepare for the material covered in the next section. Each exercise involves observing a pattern in the expanded form of the binomial expression (a + b)n.Describe the pattern for the exponents on b. (a + b)¹ = a + b (a + b)² = a² + 2ab + b² (a + b)³ = a³ +
In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form.(x2 + x-3)4
In Exercises 49–52, use the Binomial Theorem to expand each expression and write the result in simplified form. 1 1 Vx 3
In Exercises 49–52, a single die is rolled twice. Find the probability of rollinga 5 the first time and a 1 the second time.
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